Chemical corporation makes high, medium, and low grades of fuel by mixing four types of oil inputs: 1, 2, 3, and 4. The corporation wants to maximize it's daily profit. It should be noted that revenue is based only on what it's customers buy (demand), not based on what the corporation can produce. The three grades of fuel are made by blending the four inputs; however, input 2 cannot be used to make the medium grade of fuel. Each barrel of fuel is sold according to the following:

High fuel's selling price is $70.

Medium's selling price is $60.

Low's selling price is $50.

The purchase price of a barrel of oil as well as the maximum amount available to purchase is:

input 1's cost is $45 and the maximum availibility is 5000.

input 2's cost is $35 and the max. avail is 3000.

input 3's cost is $25 and the max. avail is 1000.

input 4's cost is $40 and the max avail is 500.

Each type of fuel made has minimum octane requirements as well as maximum sulfur levels. These requirements and levels are:

high's octane minimum requirement is 10. it's maximum sulfur level is 1.0%.

medium's octane minimum requirement is 9. it's max sulfur level is 2.0%

low's octane min. requirement is 8 and it's max sulfur level is 1.0%

Each oil input has average levels of octane and sulfur, and by blending these inputs, the above requirement and levels can be met:

input 1's octane rating is 12, and the sulfur content is 0.5%

input 2's octane rating is 6, sulfur content is 2%

input 3s octane rating is 9. its sulfur content is 3%

input 4's octane rating is 5 and sulfur content is 5%

The transformation cost is $4 per barrel (assume one barrel of input to one barrel of output) and the corporation can process at most 10,000 barrels per day. The corporation views the demand by its customers as strict requirements, and these demands are high's original demand is 3000 medium's is 2000 low is 1000 However, the corporation can impact this demand (positively) by advertising. For each $1 company spends on advertising a particular type of fuel, the demand increases by 12 barrels per day for that type of fuel. (Spending $100 on ads for high fuel increases demand by 1200 barrels). So total demand is the original demand plus any additional demand created with advertising. Q: Use Linear program to decide the daily processing plan? If you have a chance to buy more of input 2, would you do it?